Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×D175 |
| unambiguous semidirect product | C25⋊(D7×ΓL(1,𝔽8)) |
| Fitting, derived, Hall | C72×C25 ⋊ C2×C3 |
| Hall | C7×ΓL(1,𝔽8)×C25 ⋊ C2 |
| Hall | C7×D175 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ D25 |
| Sylow | C72 ⋊ C3×D25 |
| Sylow | C25 ⋊ D7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C72×C25 | C2×C3 |
| Frattini | C5 | ΓL(1,𝔽8)×D35 |
| socle | C5×C72 | C3×D5 |
| LCS | G ▷ C72×C25 | |
| UCS | C1 | |
51 conjugacy classes of subgroups.
445 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 60);